Grassmannian flows and applications to nonlinear partial differential equations

We show how solutions to a large class of partial differential equations with nonlocal Riccati-type nonlinearities can be generated from the corresponding linearized equations, from arbitrary initial data. It is well known that evolutionary matrix Riccati equations can be generated by projecting linear evolutionary flows on a Stiefel manifold onto a coordinate chart of the underlying Grassmann manifold. Our method relies on extending this idea to the infinite dimensional case. The key is an integral equation analogous to the Marchenko equation in integrable systems, that represents the coodinate chart map. We show explicitly how to generate such solutions to scalar partial differential equations of arbitrary order with nonlocal quadratic nonlinearities using our approach. We provide numerical simulations that demonstrate the generation of solutions to Fisher--Kolmogorov--Petrovskii--Piskunov equations with nonlocal nonlinearities. We also indicate how the method might extend to more general classes of nonlinear partial differential systems.Comment: 26 pages, 2 figure

The frequency and validity of self-reported diagnosis of Parkinson's Disease in the UK elderly: MRC CFAS cohort

BACKGROUND: Estimates of the incidence and prevalence of chronic diseases can be made using established cohort studies but these estimates may have lower reliability if based purely on self-reported diagnosis. METHODS: The MRC Cognitive Function & Ageing Study (MRC CFAS) has collected longitudinal data from a population-based random sample of 13004 individuals over the age of 65 years from 5 centres within the UK. Participants were asked at baseline and after a two-year follow-up whether they had received a diagnosis of Parkinson's disease. Our aim was to make estimates of the incidence and prevalence of PD using self-reporting, and then investigate the validity of self-reported diagnosis using other data sources where available, namely death certification and neuropathological examination. RESULTS: The self-reported prevalence of Parkinson's disease (PD) amongst these individuals increases with age from 0.7% (95%CI 0.5–0.9) for 65–75, 1.4% (95%CI 1.0–1.7) for 75–85, and 1.6% (95%CI 1.0–2.3) for 85+ age groups respectively. The overall incidence of self reported PD in this cohort was 200/100,000 per year (95%CI 144–278). Only 40% of the deceased individuals reporting prevalent PD and 35% of those reporting incident PD had diagnoses of PD recorded on their death certificates. Neuropathological examination of individuals reporting PD also showed typical PD changes in only 40%, with the remainder showing basal ganglia pathologies causing parkinsonism rather than true PD pathology. CONCLUSION: Self-reporting of PD status may be used as a screening tool to identify patients for epidemiological study, but inevitably identifies a heterogeneous group of movement disorders patients. Within this group, age, male sex, a family history of PD and reduced cigarette smoking appear to act as independent risk factors for self-reported PD

Validation of a method for identifying nursing home admissions using administrative claims

<p>Abstract</p> <p>Background</p> <p>Currently there is no standard algorithm to identify whether a subject is residing in a nursing home from administrative claims. Our objective was to develop and validate an algorithm that identifies nursing home admissions at the resident-month level using the MarketScan Medicare Supplemental and Coordination of Benefit (COB) database.</p> <p>Methods</p> <p>The computer algorithms for identifying nursing home admissions were created by using provider type, place of service, and procedure codes from the 2000 – 2002 MarketScan Medicare COB database. After the algorithms were reviewed and refined, they were compared with a detailed claims review by an expert reviewer. A random sample of 150 subjects from the claims was selected and used for the validity analysis of the algorithms. Contingency table analysis, comparison of mean differences, correlations, and t-test analyses were performed. Percentage agreement, sensitivity, specificity, and Kappa statistics were analyzed.</p> <p>Results</p> <p>The computer algorithm showed strong agreement with the expert review (99.9%) for identification of the first month of nursing home residence, with high sensitivity (96.7%), specificity (100%) and a Kappa statistic of 0.97. Weighted Pearson correlation coefficient between the algorithm and the expert review was 0.97 (<it>p </it>< 0.0001).</p> <p>Conclusion</p> <p>A reliable algorithm indicating evidence of nursing home admission was developed and validated from administrative claims data. Our algorithm can be a useful tool to identify patient transitions from and to nursing homes, as well as to screen and monitor for factors associated with nursing home admission and nursing home discharge.</p

Children at danger: injury fatalities among children in San Diego County

External causes of death are important in the pediatric population worldwide. We performed an analysis of all injury-fatalities in children between ages zero and 17 years, between January 2000 and December 2006, in San Diego County, California, United States of America. Information was obtained from the County of San Diego Medical Examiner’s database. External causes were selected and grouped by intent and mechanism. Demographics, location of death and relation between the injury mechanism and time of death were described. There were 884 medico-legal examinations, of which 480 deaths were due to external causes. There majority were males (328, 68.3%) and whites (190, 39.6%). The most prevalent mechanism of injury leading to death was road traffic accidents (40.2%), followed by asphyxia (22.7%) and penetrating trauma (17.7%). Unintentional injuries occurred in 65.8% and intentional injuries, including homicide and suicide, occurred in 24.2 and 9.4%, respectively. Death occurred at the scene in 196 cases (40.9%). Most deaths occurred in highways (35.3%) and at home (28%). One hundred forty-six patients (30.4%) died in the first 24 h. Seven percent died 1 week after the initial injury. Among the cases that died at the scene, 48.3% were motor vehicle accidents, 20.9% were victims of firearms, 6.5% died from poisoning, 5% from hanging, and 4% from drowning. External causes remain an important cause of death in children in San Diego County. Specific strategies to decrease road-traffic accidents and homicides must be developed and implemented to reduce the burden of injury-related deaths in children

Role of HPV Genotype, Multiple Infections, and Viral Load on the Risk of High-Grade Cervical Neoplasia

Background:HPV testing provides a much more sensitive method of detection for high-grade lesions than cytology, but specificity is low. Here we explore the extent to which full HPV genotyping, viral load and multiplicity of types can be used to improve specificity. Methods:A population-based sample of 47,120 women undergoing cervical screening were tested for 13 high-risk HPV genotypes. Positive predictive values (PPV) for CIN grade 2 or worse (CIN2+; N=3449) and CIN3 or worse (CIN3+; N=1475) over three years of follow-up were estimated for HPV genotype and viral load. Weighted multivariate logistic regression models were used to estimate the odds of CIN2+ or CIN3+ according to genotype, multiplicity of types and viral load. Results:High-risk HPV was detected in 15.4% of women. A hierarchy of HPV genotypes based on sequentially maximizing PPVs for CIN3+ found HPV16>33>31 to be the most predictive, followed sequentially by HPV18>35>58>45>52>59>51>39>56>68. After adjusting for higher ranked genotypes, multiple HPV infections added little to risk prediction. High viral loads for HPV18, 35, 52 and 58 carried more risk than low viral loads for HPV16, 31 and 33. High viral load for HPV16 was significantly more associated with CIN3+ than low viral load. Conclusions:HPV genotype and viral load, but not multiplicity of HPV infections, are important predictors of CIN2+ and CIN3+. Impact:The ability to identify women at higher risk of CIN2+ and CIN3+ based on both HPV genotype and viral load could be important for individualising triage plans, particularly as HPV becomes the primary screening test

Prevalence of disability in a composite ≥75 year-old population in Spain: A screening survey based on the International Classification of Functioning

<p>Abstract</p> <p>Background</p> <p>The prevalence and predictors of functional status and disability of elderly people have been studied in several European countries including Spain. However, there has been no population-based study incorporating the International Classification of Functioning, Disability and Health (ICF) framework as the basis for assessing disability. The present study reports prevalence rates for mild, moderate, and severe/extreme disability by the domains of activities and participation of the ICF.</p> <p>Methods</p> <p>Nine populations surveyed in previous prevalence studies contributed probabilistic and geographically defined samples in June 2005. The study sample was composed of 503 subjects aged ≥75 years. We implemented a two-phase screening design using the MMSE and the World Health Organization-Disability Assessment Schedule 2^ndedition (WHO-DAS II, 12 items) as cognitive and disability screening tools, respectively. Participants scoring within the positive range of the disability screening were administered the full WHO-DAS II (36 items; score range: 0-100) assessing the following areas: Understanding and communication, Getting along with people, Life activities, Getting around, Participation in society, and Self-care. Each disability area assessed by WHO-DAS II (36 items) was reported according to the ICF severity ranges (No problem, 0-4; Mild disability, 5-24; Moderate disability, 25-49; Severe/Extreme disability, 50-100).</p> <p>Results</p> <p>The age-adjusted disability prevalence figures were: 39.17 ± 2.18%, 15.31 ± 1.61%, and 10.14 ± 1.35% for mild, moderate, and severe/extreme disability, respectively. Severe and extreme disability prevalence in mobility and life activities was three times higher than the average, and highest among women. Sex variations were minimal, although life activities for women of 85 years and over had more severe/extreme disability as compared to men (OR = 5.15 95% CI 3.19-8.32).</p> <p>Conclusions</p> <p>Disability is highly prevalent among the Spanish elderly. Sex- and age-specific variations of disability are associated with particular disability domains.</p